Abstract:The solution of Schrödinger's equation leads to a high number N of independent variables. Furthermore, the restriction to (anti)symmetric functions implies some complications. We propose a sparse-grid approximation which leads to a set of non-orthogonal basis. Due to the antisymmetry, scalar products are expressed by sums of -determinants. More precisely, we have to determine where are entries of the K matrices in We propose a method to evaluate this expression such that the computational cost amounts to for fixed K, while the storage requirements are